// SPDX-License-Identifier: MIT
// SPDX-FileCopyrightText: Copyright (c) 2018, Arm Limited.

#include <math.h>
#include <stdint.h>
#include "libm.h"
#include "log2_data.h"

#define T __log2_data.tab
#define T2 __log2_data.tab2
#define B __log2_data.poly1
#define A __log2_data.poly
#define InvLn2hi __log2_data.invln2hi
#define InvLn2lo __log2_data.invln2lo
#define N (1 << LOG2_TABLE_BITS)
#define OFF 0x3fe6000000000000

/* Top 16 bits of a double.  */
static inline uint32_t top16(double x) {
  return asuint64(x) >> 48;
}

double log2(double x) {
  double_t z, r, r2, r4, y, invc, logc, kd, hi, lo, t1, t2, t3, p;
  uint64_t ix, iz, tmp;
  uint32_t top;
  int k, i;

  ix = asuint64(x);
  top = top16(x);
#define LO asuint64(1.0 - 0x1.5b51p-5)
#define HI asuint64(1.0 + 0x1.6ab2p-5)
  if (predict_false(ix - LO < HI - LO)) {
    /* Handle close to 1.0 inputs separately.  */
    /* Fix sign of zero with downward rounding when x==1.  */
    if (WANT_ROUNDING && predict_false(ix == asuint64(1.0))) {
      return 0;
    }
    r = x - 1.0;
#if __FP_FAST_FMA
    hi = r * InvLn2hi;
    lo = r * InvLn2lo + __builtin_fma(r, InvLn2hi, -hi);
#else
    double_t rhi, rlo;
    rhi = asdouble(asuint64(r) & -1ULL << 32);
    rlo = r - rhi;
    hi = rhi * InvLn2hi;
    lo = rlo * InvLn2hi + r * InvLn2lo;
#endif
    r2 = r * r; /* rounding error: 0x1p-62.  */
    r4 = r2 * r2;
    /* Worst-case error is less than 0.54 ULP (0.55 ULP without fma).  */
    p = r2 * (B[0] + r * B[1]);
    y = hi + p;
    lo += hi - y + p;
    lo += r4 * (B[2] + r * B[3] + r2 * (B[4] + r * B[5]) + r4 * (B[6] + r * B[7] + r2 * (B[8] + r * B[9])));
    y += lo;
    return eval_as_double(y);
  }
  if (predict_false(top - 0x0010 >= 0x7ff0 - 0x0010)) {
    /* x < 0x1p-1022 or inf or nan.  */
    if (ix * 2 == 0) {
      return __math_divzero(1);
    }
    if (ix == asuint64(INFINITY)) { /* log(inf) == inf.  */
      return x;
    }
    if ((top & 0x8000) || (top & 0x7ff0) == 0x7ff0) {
      return __math_invalid(x);
    }
    /* x is subnormal, normalize it.  */
    ix = asuint64(x * 0x1p52);
    ix -= 52ULL << 52;
  }

  /* x = 2^k z; where z is in range [OFF,2*OFF) and exact.
     The range is split into N subintervals.
     The ith subinterval contains z and c is near its center.  */
  tmp = ix - OFF;
  i = (tmp >> (52 - LOG2_TABLE_BITS)) % N;
  k = (int64_t)tmp >> 52; /* arithmetic shift */
  iz = ix - (tmp & 0xfffULL << 52);
  invc = T[i].invc;
  logc = T[i].logc;
  z = asdouble(iz);
  kd = (double_t)k;

  /* log2(x) = log2(z/c) + log2(c) + k.  */
  /* r ~= z/c - 1, |r| < 1/(2*N).  */
#if __FP_FAST_FMA
  /* rounding error: 0x1p-55/N.  */
  r = __builtin_fma(z, invc, -1.0);
  t1 = r * InvLn2hi;
  t2 = r * InvLn2lo + __builtin_fma(r, InvLn2hi, -t1);
#else
  double_t rhi, rlo;
  /* rounding error: 0x1p-55/N + 0x1p-65.  */
  r = (z - T2[i].chi - T2[i].clo) * invc;
  rhi = asdouble(asuint64(r) & -1ULL << 32);
  rlo = r - rhi;
  t1 = rhi * InvLn2hi;
  t2 = rlo * InvLn2hi + r * InvLn2lo;
#endif

  /* hi + lo = r/ln2 + log2(c) + k.  */
  t3 = kd + logc;
  hi = t3 + t1;
  lo = t3 - hi + t1 + t2;

  /* log2(r+1) = r/ln2 + r^2*poly(r).  */
  /* Evaluation is optimized assuming superscalar pipelined execution.  */
  r2 = r * r; /* rounding error: 0x1p-54/N^2.  */
  r4 = r2 * r2;
  /* Worst-case error if |y| > 0x1p-4: 0.547 ULP (0.550 ULP without fma).
     ~ 0.5 + 2/N/ln2 + abs-poly-error*0x1p56 ULP (+ 0.003 ULP without fma).  */
  p = A[0] + r * A[1] + r2 * (A[2] + r * A[3]) + r4 * (A[4] + r * A[5]);
  y = lo + r2 * p + hi;
  return eval_as_double(y);
}
